Logarithmic Functions and Graphs Quiz
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Questions and Answers

What is the inverse function of $f(x) = rac{1}{2} imes 3^x$?

  • $f^{-1}(x) = rac{1}{2} imes 3^x$
  • $f^{-1}(x) = rac{1}{2} imes rac{1}{3^x}$
  • $f^{-1}(x) = rac{1}{3} imes 2^x$ (correct)
  • $f^{-1}(x) = rac{1}{2} imes rac{1}{3}^x$

    • What is the vertical asymptote of the function $g(x) = 2 - rac{3}{ ext{ln}(x)}$?

  • $x = e$
  • $x = 1$
  • $x = 0$ (correct)
  • $x = -1$

    • Which of the following transformations would result in a vertical stretch of the function $h(x) = ext{log}_2(x)$?

  • $h(x) = 2 imes ext{log}_2(x)$ (correct)
  • $h(x) = -2 imes ext{log}_2(x)$
  • $h(x) = ext{log}_2(2x)$
  • $h(x) = rac{1}{2} imes ext{log}_2(x)$

    • What is the inverse function of $f(x) = e^{2x} + 1$?

    <p>$f^{-1}(x) = \log_e(x-1)$</p> Signup and view all the answers

    What is the vertical asymptote of the function $g(x) = 3 - \frac{1}{\ln(x)}$?

    <p>$x=1$</p> Signup and view all the answers

    Which of the following transformations would result in a horizontal compression of the function $h(x) = \log_3(x)$?

    <p>Replacig $x$ with $3x$ inside the function</p> Signup and view all the answers

    Which of the following transformations would result in a vertical compression of the function $f(x) = e^{2x}$?

    <p>The transformation $f(x) = e^{x/2}$</p> Signup and view all the answers

    What is the horizontal asymptote of the function $g(x) = 3 - \frac{1}{\ln(x)}$?

    <p>$y = 0$</p> Signup and view all the answers

    Which of the following transformations would result in a horizontal stretch of the function $h(x) = \log_2(x)$?

    <p>The transformation $h(x) = \log_2(2x)$</p> Signup and view all the answers

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